If the coefficient of x in the line y = ax + 3 increases, what happens to the graph?

• A. The intercept changes.
• B. The slope magnitude changes while the intercept stays at 3.
• C. The line becomes vertical.
• D. The graph remains unchanged.

Answer: (B)

The key idea is that in a line written as y = ax + b, the number multiplying x is the slope. Here the intercept is 3, so the y-intercept stays fixed at 3 no matter what a is. If you increase a, you’re making the slope steeper (its magnitude grows), so the line rises or falls more sharply as x changes, while still crossing the y-axis at y = 3. For example, with a = 1 the line goes through (0,3) and (1,4); with a = 2 it goes through (0,3) and (1,5). The intercept remains 3 in both cases, so the graph changes by becoming steeper, not by moving the intercept or becoming vertical.